First experiments: analyzing statistical differences under differing network characteristics

[venkatachalapathy]

As I see it, there are two important distributions in the original SriMil model

• wealth distribution
• proto-institution distribution (no of proto-institutions of a given size)

Expectation: Wealth distribution and proto-institution histogram should vary as we vary the network characteristic.

For example, ER model with $N$ vertices depend on the a parameter $\lambda$, the Poisson parameter of the associated degree distribution. As we vary $\lambda$, we expect the distribution to change.

Once we have a family of distributions, we could perform statistical tests to see whether differences between distributions with differing network characteristics are statistically significant.

Also, SriMil model's R code has some functions to calculate inequality in the observed wealth distribution. We should probably figure out ways to call R packages from julia.

Are you with me @WheezePuppet ?

[divilian]

I'm mostly with you. My thoughts:

• Testing the effect of different random network generation algorithms (ER, Barabasi, Watts-Strogatz, etc.) for the initial graph is mildly interesting to me. It is mildly interesting to me mostly because I love graph theory and I like playing with different kinds of graphs. However, this line of inquiry doesn't seem super-related to our main topic unless it turns out that (say) empirical levels of inequality can be reproduced when starting with a small-world network, but not an Erdos-Renyi network, or that (say) the ER parameter must exceed a certain threshold in order to produce empirical patterns of inequality. That, I agree, would be quite interesting.
• I do agree that one would not be surprised to see "change" (of an as-yet unknown type and degree) as the network generation algorithm changes. I agree it would be fairly interesting to see which graph-generation-algorithm-tweaks result in which kinds of changes.
• I assert that all the statistical analysis stuff we want to do, whether measuring inequality of wealth distros or anything else, will be eminently possible in Julia without any need to involve R. I'm about 85% confident about this, and if I turn out to be wrong, and it's actually easier to outsource something to R rather than code it up ourselves in Julia, we can do as you suggest.

[venkatachalapathy]

Since we expect, within family and between family variations in the size of established proto-institutions and resulting wealth distributions, I would like to have plots that show how, for example, as the Poission parameter of a ER graph varies, the distributions of interest change.

Isn't this going to answer the question of how social network changes influences inequality?

[divilian]

Okay, I see what you mean. Yeah, I guess that does partially get at an important question.

One comment I'll make is that I'm generally more interested in dynamic graphs -- i.e., social networks which evolve as the simulation proceeds, by forming and breaking links -- than in how the initial graph is formed. Currently, our graph is static (with one exception: when two unconnected nodes meet by chance and form a proto, at which point a link is added between them).

My point is that "starting with an exogenous ER and running our simulation-that-doesn't-change-the-graph" vs. "starting with an exogenous Watts-Strogatz and running it" might not be the most fruitful comparison to make in answering the question of how social network changes influence inequality. Perhaps better is "starting with an exogeneous ER and endogeneously evolving the graph according to rules X" vs. "starting with an exogenous ER and endogeneously using rules Y."

[venkatachalapathy]

Ah, I see. I see the system differently than you. We need to arrive at a common understanding of the model.

I'll read your slides and your before I can say further. I've been playing with julia myself. So, it will be a good exercise.

[divilian]

We need to arrive at a common understanding of the model.

Wanna Zoom?

[venkatachalapathy]

Unfortunately, I use my kid's tablet to zoom and the tablet is safe at home. We could do an old fashioned phone call today.

[venkatachalapathy]

OK. I read through your code and the slides. Some thoughts

• Your random connection to non-neighbors provide a dynamics that is one step removed from my vanilla model
• I see this as a next step

In my vanilla model

• $o$ is $0$.
• Network formation takes place before the wealth accumulation activity begins
• This network formation uses some sociological theory to assign relations between the actors
• Agents interact and form proto-institutions only with the neighbors

[divilian]

Okay, agreed that setting $o$ to 0 is a limiting case, and we can analyze that in isolation first.

If I understand it, I believe your second bullet is also true of the current Julia model (with the aforementioned exception when $o$>0).

When you say "assign relations between the actors" do you merely mean "decide who has a connection to whom" or do you mean "there are different types and/or strengths of connections?"

[venkatachalapathy]

Yes, I think so.

Yes, whether the actors have connections, for now. Eventually extendable to labeling actors and other things.

[divilian]

Okay, cool. I'm excited to hear about the sociological theory that will inform the model about which agents should be initially connected to whom.

[divilian]

Assigning the "allow initial graphs other than the simple ER model" portion of this task to @will-nehrboss.

[divilian]

Given the param_sweep.jl file that @will-nehrboss just added, I think we're mostly in a position to do this now.

[venkatachalapathy]

We are using a confidence interval based approach for CSSA19. The bootstrapped two-sample test, if it is necessary at all, is now a phase 2+ issue. @WheezePuppet could you remove the phase 1 label?